Suppose a consumer's utility function is U(F₀,F₁)= F₀^0.5F₁^0.5,where F₀ represents food consumed this year and F₁ represents food consumed next year.For that utility function,the marginal utility of food consumed this year is 0.5 × (F₁/F₀)^0.5 and the marginal utility of food consumed next year is 0.5 × (F₀/F₁)^0.5.Suppose the consumer earns $100 this year and nothing in the next,food costs $1 per unit in both years,and the interest rate is 10%.How much food does she consume this year,and how much does consume tomorrow? A) She consumes 45 units of food this year and 55 units of food next year. B) She consumes 50 units of food this year and 50 units of food next year. C) She consumes 55 units of food this year and 50 units of food next year. D) She consumes 50 units of food this year and 55 units of food next year.

Question

Quizplus · Accepted Answer

Since the interest rate is 10%, the present value of $100 one year from now is $90.91 ($100/(1+10%)). We can set up the following optimization problem: max F₀^0.5, F₁^0.5 subject to: P1 × F₀ + P2 × F₁ ≤ $100 P1 × F₀ + P2 × F₁/1.1 = $90.91 where P1 and P2 are the prices of food in year 1 and year 2 respectively. Solving this problem gives us F₀ = 50 and F₁ = 55, so the consumer consumes 50 units of food this year and 55 units of food next year. Therefore, the answer is D.

Suppose a Consumer's Utility Function Is U(F0,F1)= F00

Suppose a Consumer's Utility Function Is U(F₀,F₁)= F₀⁰